Actual source code: parabolic.c
petsc-3.12.5 2020-03-29
1: #include <petsc/private/taoimpl.h>
3: /*T
4: Concepts: TAO^Solving a system of nonlinear equations, nonlinear least squares
5: Routines: TaoCreate();
6: Routines: TaoSetType();
7: Routines: TaoSetInitialVector();
8: Routines: TaoSetObjectiveRoutine();
9: Routines: TaoSetGradientRoutine();
10: Routines: TaoSetConstraintsRoutine();
11: Routines: TaoSetJacobianStateRoutine();
12: Routines: TaoSetJacobianDesignRoutine();
13: Routines: TaoSetStateDesignIS();
14: Routines: TaoSetFromOptions();
15: Routines: TaoSolve();
16: Routines: TaoDestroy();
17: Processors: n
18: T*/
22: typedef struct {
23: PetscInt n; /* Number of variables */
24: PetscInt m; /* Number of constraints per time step */
25: PetscInt mx; /* grid points in each direction */
26: PetscInt nt; /* Number of time steps; as of now, must be divisible by 8 */
27: PetscInt ndata; /* Number of data points per sample */
28: PetscInt ns; /* Number of samples */
29: PetscInt *sample_times; /* Times of samples */
30: IS s_is;
31: IS d_is;
33: VecScatter state_scatter;
34: VecScatter design_scatter;
35: VecScatter *yi_scatter;
36: VecScatter *di_scatter;
38: Mat Js,Jd,JsBlockPrec,JsInv,JsBlock;
39: PetscBool jformed,dsg_formed;
41: PetscReal alpha; /* Regularization parameter */
42: PetscReal beta; /* Weight attributed to ||u||^2 in regularization functional */
43: PetscReal noise; /* Amount of noise to add to data */
44: PetscReal ht; /* Time step */
46: Mat Qblock,QblockT;
47: Mat L,LT;
48: Mat Div,Divwork;
49: Mat Grad;
50: Mat Av,Avwork,AvT;
51: Mat DSG;
52: Vec q;
53: Vec ur; /* reference */
55: Vec d;
56: Vec dwork;
57: Vec *di;
59: Vec y; /* state variables */
60: Vec ywork;
62: Vec ytrue;
63: Vec *yi,*yiwork;
65: Vec u; /* design variables */
66: Vec uwork;
68: Vec utrue;
69: Vec js_diag;
70: Vec c; /* constraint vector */
71: Vec cwork;
73: Vec lwork;
74: Vec S;
75: Vec Rwork,Swork,Twork;
76: Vec Av_u;
78: KSP solver;
79: PC prec;
81: PetscInt ksp_its;
82: PetscInt ksp_its_initial;
83: } AppCtx;
86: PetscErrorCode FormFunction(Tao, Vec, PetscReal*, void*);
87: PetscErrorCode FormGradient(Tao, Vec, Vec, void*);
88: PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal*, Vec, void*);
89: PetscErrorCode FormJacobianState(Tao, Vec, Mat, Mat, Mat, void*);
90: PetscErrorCode FormJacobianDesign(Tao, Vec, Mat, void*);
91: PetscErrorCode FormConstraints(Tao, Vec, Vec, void*);
92: PetscErrorCode FormHessian(Tao, Vec, Mat, Mat, void*);
93: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat);
94: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat);
95: PetscErrorCode ParabolicInitialize(AppCtx *user);
96: PetscErrorCode ParabolicDestroy(AppCtx *user);
97: PetscErrorCode ParabolicMonitor(Tao, void*);
99: PetscErrorCode StateMatMult(Mat,Vec,Vec);
100: PetscErrorCode StateMatBlockMult(Mat,Vec,Vec);
101: PetscErrorCode StateMatMultTranspose(Mat,Vec,Vec);
102: PetscErrorCode StateMatGetDiagonal(Mat,Vec);
103: PetscErrorCode StateMatDuplicate(Mat,MatDuplicateOption,Mat*);
104: PetscErrorCode StateMatInvMult(Mat,Vec,Vec);
105: PetscErrorCode StateMatInvTransposeMult(Mat,Vec,Vec);
106: PetscErrorCode StateMatBlockPrecMult(PC,Vec,Vec);
108: PetscErrorCode DesignMatMult(Mat,Vec,Vec);
109: PetscErrorCode DesignMatMultTranspose(Mat,Vec,Vec);
111: PetscErrorCode Gather_i(Vec,Vec*,VecScatter*,PetscInt);
112: PetscErrorCode Scatter_i(Vec,Vec*,VecScatter*,PetscInt);
114: static char help[]="";
116: int main(int argc, char **argv)
117: {
118: PetscErrorCode ierr;
119: Vec x,x0;
120: Tao tao;
121: AppCtx user;
122: IS is_allstate,is_alldesign;
123: PetscInt lo,hi,hi2,lo2,ksp_old;
124: PetscInt ntests = 1;
125: PetscInt i;
126: #if defined(PETSC_USE_LOG)
127: PetscLogStage stages[1];
128: #endif
130: PetscInitialize(&argc, &argv, (char*)0,help);if (ierr) return ierr;
131: user.mx = 8;
132: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,NULL,NULL);
133: PetscOptionsInt("-mx","Number of grid points in each direction","",user.mx,&user.mx,NULL);
134: user.nt = 8;
135: PetscOptionsInt("-nt","Number of time steps","",user.nt,&user.nt,NULL);
136: user.ndata = 64;
137: PetscOptionsInt("-ndata","Numbers of data points per sample","",user.ndata,&user.ndata,NULL);
138: user.ns = 8;
139: PetscOptionsInt("-ns","Number of samples","",user.ns,&user.ns,NULL);
140: user.alpha = 1.0;
141: PetscOptionsReal("-alpha","Regularization parameter","",user.alpha,&user.alpha,NULL);
142: user.beta = 0.01;
143: PetscOptionsReal("-beta","Weight attributed to ||u||^2 in regularization functional","",user.beta,&user.beta,NULL);
144: user.noise = 0.01;
145: PetscOptionsReal("-noise","Amount of noise to add to data","",user.noise,&user.noise,NULL);
147: user.m = user.mx*user.mx*user.mx; /* number of constraints per time step */
148: user.n = user.m*(user.nt+1); /* number of variables */
149: user.ht = (PetscReal)1/user.nt;
151: VecCreate(PETSC_COMM_WORLD,&user.u);
152: VecCreate(PETSC_COMM_WORLD,&user.y);
153: VecCreate(PETSC_COMM_WORLD,&user.c);
154: VecSetSizes(user.u,PETSC_DECIDE,user.n-user.m*user.nt);
155: VecSetSizes(user.y,PETSC_DECIDE,user.m*user.nt);
156: VecSetSizes(user.c,PETSC_DECIDE,user.m*user.nt);
157: VecSetFromOptions(user.u);
158: VecSetFromOptions(user.y);
159: VecSetFromOptions(user.c);
161: /* Create scatters for reduced spaces.
162: If the state vector y and design vector u are partitioned as
163: [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
164: then the solution vector x is organized as
165: [y_1; u_1; y_2; u_2; ...; y_np; u_np].
166: The index sets user.s_is and user.d_is correspond to the indices of the
167: state and design variables owned by the current processor.
168: */
169: VecCreate(PETSC_COMM_WORLD,&x);
171: VecGetOwnershipRange(user.y,&lo,&hi);
172: VecGetOwnershipRange(user.u,&lo2,&hi2);
174: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_allstate);
175: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+lo2,1,&user.s_is);
177: ISCreateStride(PETSC_COMM_SELF,hi2-lo2,lo2,1,&is_alldesign);
178: ISCreateStride(PETSC_COMM_SELF,hi2-lo2,hi+lo2,1,&user.d_is);
180: VecSetSizes(x,hi-lo+hi2-lo2,user.n);
181: VecSetFromOptions(x);
183: VecScatterCreate(x,user.s_is,user.y,is_allstate,&user.state_scatter);
184: VecScatterCreate(x,user.d_is,user.u,is_alldesign,&user.design_scatter);
185: ISDestroy(&is_alldesign);
186: ISDestroy(&is_allstate);
188: /* Create TAO solver and set desired solution method */
189: TaoCreate(PETSC_COMM_WORLD,&tao);
190: TaoSetType(tao,TAOLCL);
192: /* Set up initial vectors and matrices */
193: ParabolicInitialize(&user);
195: Gather(x,user.y,user.state_scatter,user.u,user.design_scatter);
196: VecDuplicate(x,&x0);
197: VecCopy(x,x0);
199: /* Set solution vector with an initial guess */
200: TaoSetInitialVector(tao,x);
201: TaoSetObjectiveRoutine(tao, FormFunction, (void *)&user);
202: TaoSetGradientRoutine(tao, FormGradient, (void *)&user);
203: TaoSetConstraintsRoutine(tao, user.c, FormConstraints, (void *)&user);
205: TaoSetJacobianStateRoutine(tao, user.Js, user.JsBlockPrec, user.JsInv, FormJacobianState, (void *)&user);
206: TaoSetJacobianDesignRoutine(tao, user.Jd, FormJacobianDesign, (void *)&user);
208: TaoSetFromOptions(tao);
209: TaoSetStateDesignIS(tao,user.s_is,user.d_is);
211: /* SOLVE THE APPLICATION */
212: PetscOptionsInt("-ntests","Number of times to repeat TaoSolve","",ntests,&ntests,NULL);
213: PetscOptionsEnd();
214: PetscLogStageRegister("Trials",&stages[0]);
215: PetscLogStagePush(stages[0]);
216: user.ksp_its_initial = user.ksp_its;
217: ksp_old = user.ksp_its;
218: for (i=0; i<ntests; i++){
219: TaoSolve(tao);
220: PetscPrintf(PETSC_COMM_WORLD,"KSP Iterations = %D\n",user.ksp_its-ksp_old);
221: VecCopy(x0,x);
222: TaoSetInitialVector(tao,x);
223: }
224: PetscLogStagePop();
225: PetscBarrier((PetscObject)x);
226: PetscPrintf(PETSC_COMM_WORLD,"KSP iterations within initialization: ");
227: PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its_initial);
228: PetscPrintf(PETSC_COMM_WORLD,"Total KSP iterations over %D trial(s): ",ntests);
229: PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its);
230: PetscPrintf(PETSC_COMM_WORLD,"KSP iterations per trial: ");
231: PetscPrintf(PETSC_COMM_WORLD,"%D\n",(user.ksp_its-user.ksp_its_initial)/ntests);
233: TaoDestroy(&tao);
234: VecDestroy(&x);
235: VecDestroy(&x0);
236: ParabolicDestroy(&user);
238: PetscFinalize();
239: return ierr;
240: }
241: /* ------------------------------------------------------------------- */
242: /*
243: dwork = Qy - d
244: lwork = L*(u-ur)
245: f = 1/2 * (dwork.dork + alpha*lwork.lwork)
246: */
247: PetscErrorCode FormFunction(Tao tao,Vec X,PetscReal *f,void *ptr)
248: {
250: PetscReal d1=0,d2=0;
251: PetscInt i,j;
252: AppCtx *user = (AppCtx*)ptr;
255: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
256: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
257: for (j=0; j<user->ns; j++){
258: i = user->sample_times[j];
259: MatMult(user->Qblock,user->yi[i],user->di[j]);
260: }
261: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
262: VecAXPY(user->dwork,-1.0,user->d);
263: VecDot(user->dwork,user->dwork,&d1);
265: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
266: MatMult(user->L,user->uwork,user->lwork);
267: VecDot(user->lwork,user->lwork,&d2);
269: *f = 0.5 * (d1 + user->alpha*d2);
270: return(0);
271: }
273: /* ------------------------------------------------------------------- */
274: /*
275: state: g_s = Q' *(Qy - d)
276: design: g_d = alpha*L'*L*(u-ur)
277: */
278: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
279: {
281: PetscInt i,j;
282: AppCtx *user = (AppCtx*)ptr;
285: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
286: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
287: for (j=0; j<user->ns; j++){
288: i = user->sample_times[j];
289: MatMult(user->Qblock,user->yi[i],user->di[j]);
290: }
291: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
292: VecAXPY(user->dwork,-1.0,user->d);
293: Scatter_i(user->dwork,user->di,user->di_scatter,user->ns);
294: VecSet(user->ywork,0.0);
295: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
296: for (j=0; j<user->ns; j++){
297: i = user->sample_times[j];
298: MatMult(user->QblockT,user->di[j],user->yiwork[i]);
299: }
300: Gather_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
302: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
303: MatMult(user->L,user->uwork,user->lwork);
304: MatMult(user->LT,user->lwork,user->uwork);
305: VecScale(user->uwork, user->alpha);
306: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
307: return(0);
308: }
310: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
311: {
313: PetscReal d1,d2;
314: PetscInt i,j;
315: AppCtx *user = (AppCtx*)ptr;
318: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
319: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
320: for (j=0; j<user->ns; j++){
321: i = user->sample_times[j];
322: MatMult(user->Qblock,user->yi[i],user->di[j]);
323: }
324: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
325: VecAXPY(user->dwork,-1.0,user->d);
326: VecDot(user->dwork,user->dwork,&d1);
327: Scatter_i(user->dwork,user->di,user->di_scatter,user->ns);
328: VecSet(user->ywork,0.0);
329: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
330: for (j=0; j<user->ns; j++){
331: i = user->sample_times[j];
332: MatMult(user->QblockT,user->di[j],user->yiwork[i]);
333: }
334: Gather_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
336: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
337: MatMult(user->L,user->uwork,user->lwork);
338: VecDot(user->lwork,user->lwork,&d2);
339: MatMult(user->LT,user->lwork,user->uwork);
340: VecScale(user->uwork, user->alpha);
341: *f = 0.5 * (d1 + user->alpha*d2);
343: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
344: return(0);
345: }
347: /* ------------------------------------------------------------------- */
348: /* A
349: MatShell object
350: */
351: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
352: {
354: AppCtx *user = (AppCtx*)ptr;
357: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
358: VecSet(user->uwork,0);
359: VecAXPY(user->uwork,-1.0,user->u);
360: VecExp(user->uwork);
361: MatMult(user->Av,user->uwork,user->Av_u);
362: VecCopy(user->Av_u,user->Swork);
363: VecReciprocal(user->Swork);
364: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
365: MatDiagonalScale(user->Divwork,NULL,user->Swork);
366: if (user->dsg_formed) {
367: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
368: } else {
369: MatMatMultSymbolic(user->Divwork,user->Grad,PETSC_DECIDE,&user->DSG);
370: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
371: user->dsg_formed = PETSC_TRUE;
372: }
374: /* B = speye(nx^3) + ht*DSG; */
375: MatScale(user->DSG,user->ht);
376: MatShift(user->DSG,1.0);
377: return(0);
378: }
380: /* ------------------------------------------------------------------- */
381: /* B */
382: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
383: {
385: AppCtx *user = (AppCtx*)ptr;
388: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
389: return(0);
390: }
392: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
393: {
395: PetscInt i;
396: AppCtx *user;
399: MatShellGetContext(J_shell,(void**)&user);
400: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
401: MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);
402: for (i=1; i<user->nt; i++){
403: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
404: VecAXPY(user->yiwork[i],-1.0,user->yi[i-1]);
405: }
406: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
407: return(0);
408: }
410: PetscErrorCode StateMatMultTranspose(Mat J_shell, Vec X, Vec Y)
411: {
413: PetscInt i;
414: AppCtx *user;
417: MatShellGetContext(J_shell,(void**)&user);
418: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
419: for (i=0; i<user->nt-1; i++){
420: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
421: VecAXPY(user->yiwork[i],-1.0,user->yi[i+1]);
422: }
423: i = user->nt-1;
424: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
425: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
426: return(0);
427: }
429: PetscErrorCode StateMatBlockMult(Mat J_shell, Vec X, Vec Y)
430: {
432: AppCtx *user;
435: MatShellGetContext(J_shell,(void**)&user);
436: MatMult(user->Grad,X,user->Swork);
437: VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
438: MatMult(user->Div,user->Swork,Y);
439: VecAYPX(Y,user->ht,X);
440: return(0);
441: }
443: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
444: {
446: PetscInt i;
447: AppCtx *user;
450: MatShellGetContext(J_shell,(void**)&user);
452: /* sdiag(1./v) */
453: VecSet(user->uwork,0);
454: VecAXPY(user->uwork,-1.0,user->u);
455: VecExp(user->uwork);
457: /* sdiag(1./((Av*(1./v)).^2)) */
458: MatMult(user->Av,user->uwork,user->Swork);
459: VecPointwiseMult(user->Swork,user->Swork,user->Swork);
460: VecReciprocal(user->Swork);
462: /* (Av * (sdiag(1./v) * b)) */
463: VecPointwiseMult(user->uwork,user->uwork,X);
464: MatMult(user->Av,user->uwork,user->Twork);
466: /* (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b))) */
467: VecPointwiseMult(user->Swork,user->Twork,user->Swork);
469: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
470: for (i=0; i<user->nt; i++){
471: /* (sdiag(Grad*y(:,i)) */
472: MatMult(user->Grad,user->yi[i],user->Twork);
474: /* ht * Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
475: VecPointwiseMult(user->Twork,user->Twork,user->Swork);
476: MatMult(user->Div,user->Twork,user->yiwork[i]);
477: VecScale(user->yiwork[i],user->ht);
478: }
479: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
481: return(0);
482: }
484: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
485: {
487: PetscInt i;
488: AppCtx *user;
491: MatShellGetContext(J_shell,(void**)&user);
493: /* sdiag(1./((Av*(1./v)).^2)) */
494: VecSet(user->uwork,0);
495: VecAXPY(user->uwork,-1.0,user->u);
496: VecExp(user->uwork);
497: MatMult(user->Av,user->uwork,user->Rwork);
498: VecPointwiseMult(user->Rwork,user->Rwork,user->Rwork);
499: VecReciprocal(user->Rwork);
501: VecSet(Y,0.0);
502: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
503: Scatter_i(X,user->yiwork,user->yi_scatter,user->nt);
504: for (i=0; i<user->nt; i++){
505: /* (Div' * b(:,i)) */
506: MatMult(user->Grad,user->yiwork[i],user->Swork);
508: /* sdiag(Grad*y(:,i)) */
509: MatMult(user->Grad,user->yi[i],user->Twork);
511: /* (sdiag(Grad*y(:,i)) * (Div' * b(:,i))) */
512: VecPointwiseMult(user->Twork,user->Swork,user->Twork);
514: /* (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i)))) */
515: VecPointwiseMult(user->Twork,user->Rwork,user->Twork);
517: /* (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
518: MatMult(user->AvT,user->Twork,user->yiwork[i]);
520: /* sdiag(1./v) * (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
521: VecPointwiseMult(user->yiwork[i],user->uwork,user->yiwork[i]);
522: VecAXPY(Y,user->ht,user->yiwork[i]);
523: }
524: return(0);
525: }
527: PetscErrorCode StateMatBlockPrecMult(PC PC_shell, Vec X, Vec Y)
528: {
530: AppCtx *user;
533: PCShellGetContext(PC_shell,(void**)&user);
535: if (user->dsg_formed) {
536: MatSOR(user->DSG,X,1.0,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP),0.0,1,1,Y);
537: } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"DSG not formed");
538: return(0);
539: }
541: PetscErrorCode StateMatInvMult(Mat J_shell, Vec X, Vec Y)
542: {
544: AppCtx *user;
545: PetscInt its,i;
548: MatShellGetContext(J_shell,(void**)&user);
550: if (Y == user->ytrue) {
551: /* First solve is done with true solution to set up problem */
552: KSPSetTolerances(user->solver,1e-8,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
553: } else {
554: KSPSetTolerances(user->solver,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
555: }
557: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
558: KSPSolve(user->solver,user->yi[0],user->yiwork[0]);
559: KSPGetIterationNumber(user->solver,&its);
560: user->ksp_its = user->ksp_its + its;
562: for (i=1; i<user->nt; i++){
563: VecAXPY(user->yi[i],1.0,user->yiwork[i-1]);
564: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
565: KSPGetIterationNumber(user->solver,&its);
566: user->ksp_its = user->ksp_its + its;
567: }
568: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
569: return(0);
570: }
572: PetscErrorCode StateMatInvTransposeMult(Mat J_shell, Vec X, Vec Y)
573: {
575: AppCtx *user;
576: PetscInt its,i;
579: MatShellGetContext(J_shell,(void**)&user);
581: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
583: i = user->nt - 1;
584: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
586: KSPGetIterationNumber(user->solver,&its);
587: user->ksp_its = user->ksp_its + its;
589: for (i=user->nt-2; i>=0; i--){
590: VecAXPY(user->yi[i],1.0,user->yiwork[i+1]);
591: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
593: KSPGetIterationNumber(user->solver,&its);
594: user->ksp_its = user->ksp_its + its;
596: }
598: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
599: return(0);
600: }
602: PetscErrorCode StateMatDuplicate(Mat J_shell, MatDuplicateOption opt, Mat *new_shell)
603: {
605: AppCtx *user;
608: MatShellGetContext(J_shell,(void**)&user);
610: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,new_shell);
611: MatShellSetOperation(*new_shell,MATOP_MULT,(void(*)(void))StateMatMult);
612: MatShellSetOperation(*new_shell,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
613: MatShellSetOperation(*new_shell,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
614: MatShellSetOperation(*new_shell,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
615: return(0);
616: }
618: PetscErrorCode StateMatGetDiagonal(Mat J_shell, Vec X)
619: {
621: AppCtx *user;
624: MatShellGetContext(J_shell,(void**)&user);
625: VecCopy(user->js_diag,X);
626: return(0);
628: }
630: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
631: {
632: /* con = Ay - q, A = [B 0 0 ... 0;
633: -I B 0 ... 0;
634: 0 -I B ... 0;
635: ... ;
636: 0 ... -I B]
637: B = ht * Div * Sigma * Grad + eye */
639: PetscInt i;
640: AppCtx *user = (AppCtx*)ptr;
643: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
644: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
645: MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);
646: for (i=1; i<user->nt; i++){
647: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
648: VecAXPY(user->yiwork[i],-1.0,user->yi[i-1]);
649: }
650: Gather_i(C,user->yiwork,user->yi_scatter,user->nt);
651: VecAXPY(C,-1.0,user->q);
652: return(0);
653: }
656: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
657: {
661: VecScatterBegin(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
662: VecScatterEnd(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
663: VecScatterBegin(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
664: VecScatterEnd(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
665: return(0);
666: }
668: PetscErrorCode Scatter_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
669: {
671: PetscInt i;
674: for (i=0; i<nt; i++){
675: VecScatterBegin(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
676: VecScatterEnd(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
677: }
678: return(0);
679: }
682: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
683: {
687: VecScatterBegin(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
688: VecScatterEnd(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
689: VecScatterBegin(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
690: VecScatterEnd(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
691: return(0);
692: }
694: PetscErrorCode Gather_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
695: {
697: PetscInt i;
700: for (i=0; i<nt; i++){
701: VecScatterBegin(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
702: VecScatterEnd(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
703: }
704: return(0);
705: }
707: PetscErrorCode ParabolicInitialize(AppCtx *user)
708: {
710: PetscInt m,n,i,j,k,linear_index,istart,iend,iblock,lo,hi,lo2,hi2;
711: Vec XX,YY,ZZ,XXwork,YYwork,ZZwork,UTwork,yi,di,bc;
712: PetscReal *x, *y, *z;
713: PetscReal h,stime;
714: PetscScalar hinv,neg_hinv,half = 0.5,sqrt_beta;
715: PetscInt im,indx1,indx2,indy1,indy2,indz1,indz2,nx,ny,nz;
716: PetscReal xri,yri,zri,xim,yim,zim,dx1,dx2,dy1,dy2,dz1,dz2,Dx,Dy,Dz;
717: PetscScalar v,vx,vy,vz;
718: IS is_from_y,is_to_yi,is_from_d,is_to_di;
719: /* Data locations */
720: PetscScalar xr[64] = {0.4970, 0.8498, 0.7814, 0.6268, 0.7782, 0.6402, 0.3617, 0.3160,
721: 0.3610, 0.5298, 0.6987, 0.3331, 0.7962, 0.5596, 0.3866, 0.6774,
722: 0.5407, 0.4518, 0.6702, 0.6061, 0.7580, 0.8997, 0.5198, 0.8326,
723: 0.2138, 0.9198, 0.3000, 0.2833, 0.8288, 0.7076, 0.1820, 0.0728,
724: 0.8447, 0.2367, 0.3239, 0.6413, 0.3114, 0.4731, 0.1192, 0.9273,
725: 0.5724, 0.4331, 0.5136, 0.3547, 0.4413, 0.2602, 0.5698, 0.7278,
726: 0.5261, 0.6230, 0.2454, 0.3948, 0.7479, 0.6582, 0.4660, 0.5594,
727: 0.7574, 0.1143, 0.5900, 0.1065, 0.4260, 0.3294, 0.8276, 0.0756};
729: PetscScalar yr[64] = {0.7345, 0.9120, 0.9288, 0.7528, 0.4463, 0.4985, 0.2497, 0.6256,
730: 0.3425, 0.9026, 0.6983, 0.4230, 0.7140, 0.2970, 0.4474, 0.8792,
731: 0.6604, 0.2485, 0.7968, 0.6127, 0.1796, 0.2437, 0.5938, 0.6137,
732: 0.3867, 0.5658, 0.4575, 0.1009, 0.0863, 0.3361, 0.0738, 0.3985,
733: 0.6602, 0.1437, 0.0934, 0.5983, 0.5950, 0.0763, 0.0768, 0.2288,
734: 0.5761, 0.1129, 0.3841, 0.6150, 0.6904, 0.6686, 0.1361, 0.4601,
735: 0.4491, 0.3716, 0.1969, 0.6537, 0.6743, 0.6991, 0.4811, 0.5480,
736: 0.1684, 0.4569, 0.6889, 0.8437, 0.3015, 0.2854, 0.8199, 0.2658};
738: PetscScalar zr[64] = {0.7668, 0.8573, 0.2654, 0.2719, 0.1060, 0.1311, 0.6232, 0.2295,
739: 0.8009, 0.2147, 0.2119, 0.9325, 0.4473, 0.3600, 0.3374, 0.3819,
740: 0.4066, 0.5801, 0.1673, 0.0959, 0.4638, 0.8236, 0.8800, 0.2939,
741: 0.2028, 0.8262, 0.2706, 0.6276, 0.9085, 0.6443, 0.8241, 0.0712,
742: 0.1824, 0.7789, 0.4389, 0.8415, 0.7055, 0.6639, 0.3653, 0.2078,
743: 0.1987, 0.2297, 0.4321, 0.8115, 0.4915, 0.7764, 0.4657, 0.4627,
744: 0.4569, 0.4232, 0.8514, 0.0674, 0.3227, 0.1055, 0.6690, 0.6313,
745: 0.9226, 0.5461, 0.4126, 0.2364, 0.6096, 0.7042, 0.3914, 0.0711};
748: PetscMalloc1(user->mx,&x);
749: PetscMalloc1(user->mx,&y);
750: PetscMalloc1(user->mx,&z);
751: user->jformed = PETSC_FALSE;
752: user->dsg_formed = PETSC_FALSE;
754: n = user->mx * user->mx * user->mx;
755: m = 3 * user->mx * user->mx * (user->mx-1);
756: sqrt_beta = PetscSqrtScalar(user->beta);
758: user->ksp_its = 0;
759: user->ksp_its_initial = 0;
761: stime = (PetscReal)user->nt/user->ns;
762: PetscMalloc1(user->ns,&user->sample_times);
763: for (i=0; i<user->ns; i++){
764: user->sample_times[i] = (PetscInt)(stime*((PetscReal)i+1.0)-0.5);
765: }
767: VecCreate(PETSC_COMM_WORLD,&XX);
768: VecCreate(PETSC_COMM_WORLD,&user->q);
769: VecSetSizes(XX,PETSC_DECIDE,n);
770: VecSetSizes(user->q,PETSC_DECIDE,n*user->nt);
771: VecSetFromOptions(XX);
772: VecSetFromOptions(user->q);
774: VecDuplicate(XX,&YY);
775: VecDuplicate(XX,&ZZ);
776: VecDuplicate(XX,&XXwork);
777: VecDuplicate(XX,&YYwork);
778: VecDuplicate(XX,&ZZwork);
779: VecDuplicate(XX,&UTwork);
780: VecDuplicate(XX,&user->utrue);
781: VecDuplicate(XX,&bc);
783: /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
784: h = 1.0/user->mx;
785: hinv = user->mx;
786: neg_hinv = -hinv;
788: VecGetOwnershipRange(XX,&istart,&iend);
789: for (linear_index=istart; linear_index<iend; linear_index++){
790: i = linear_index % user->mx;
791: j = ((linear_index-i)/user->mx) % user->mx;
792: k = ((linear_index-i)/user->mx-j) / user->mx;
793: vx = h*(i+0.5);
794: vy = h*(j+0.5);
795: vz = h*(k+0.5);
796: VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
797: VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
798: VecSetValues(ZZ,1,&linear_index,&vz,INSERT_VALUES);
799: if ((vx<0.6) && (vx>0.4) && (vy<0.6) && (vy>0.4) && (vy<0.6) && (vz<0.6) && (vz>0.4)){
800: v = 1000.0;
801: VecSetValues(bc,1,&linear_index,&v,INSERT_VALUES);
802: }
803: }
805: VecAssemblyBegin(XX);
806: VecAssemblyEnd(XX);
807: VecAssemblyBegin(YY);
808: VecAssemblyEnd(YY);
809: VecAssemblyBegin(ZZ);
810: VecAssemblyEnd(ZZ);
811: VecAssemblyBegin(bc);
812: VecAssemblyEnd(bc);
814: /* Compute true parameter function
815: ut = 0.5 + exp(-10*((x-0.5)^2+(y-0.5)^2+(z-0.5)^2)) */
816: VecCopy(XX,XXwork);
817: VecCopy(YY,YYwork);
818: VecCopy(ZZ,ZZwork);
820: VecShift(XXwork,-0.5);
821: VecShift(YYwork,-0.5);
822: VecShift(ZZwork,-0.5);
824: VecPointwiseMult(XXwork,XXwork,XXwork);
825: VecPointwiseMult(YYwork,YYwork,YYwork);
826: VecPointwiseMult(ZZwork,ZZwork,ZZwork);
828: VecCopy(XXwork,user->utrue);
829: VecAXPY(user->utrue,1.0,YYwork);
830: VecAXPY(user->utrue,1.0,ZZwork);
831: VecScale(user->utrue,-10.0);
832: VecExp(user->utrue);
833: VecShift(user->utrue,0.5);
835: VecDestroy(&XX);
836: VecDestroy(&YY);
837: VecDestroy(&ZZ);
838: VecDestroy(&XXwork);
839: VecDestroy(&YYwork);
840: VecDestroy(&ZZwork);
841: VecDestroy(&UTwork);
843: /* Initial guess and reference model */
844: VecDuplicate(user->utrue,&user->ur);
845: VecSet(user->ur,0.0);
847: /* Generate Grad matrix */
848: MatCreate(PETSC_COMM_WORLD,&user->Grad);
849: MatSetSizes(user->Grad,PETSC_DECIDE,PETSC_DECIDE,m,n);
850: MatSetFromOptions(user->Grad);
851: MatMPIAIJSetPreallocation(user->Grad,2,NULL,2,NULL);
852: MatSeqAIJSetPreallocation(user->Grad,2,NULL);
853: MatGetOwnershipRange(user->Grad,&istart,&iend);
855: for (i=istart; i<iend; i++){
856: if (i<m/3){
857: iblock = i / (user->mx-1);
858: j = iblock*user->mx + (i % (user->mx-1));
859: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
860: j = j+1;
861: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
862: }
863: if (i>=m/3 && i<2*m/3){
864: iblock = (i-m/3) / (user->mx*(user->mx-1));
865: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
866: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
867: j = j + user->mx;
868: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
869: }
870: if (i>=2*m/3){
871: j = i-2*m/3;
872: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
873: j = j + user->mx*user->mx;
874: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
875: }
876: }
878: MatAssemblyBegin(user->Grad,MAT_FINAL_ASSEMBLY);
879: MatAssemblyEnd(user->Grad,MAT_FINAL_ASSEMBLY);
882: /* Generate arithmetic averaging matrix Av */
883: MatCreate(PETSC_COMM_WORLD,&user->Av);
884: MatSetSizes(user->Av,PETSC_DECIDE,PETSC_DECIDE,m,n);
885: MatSetFromOptions(user->Av);
886: MatMPIAIJSetPreallocation(user->Av,2,NULL,2,NULL);
887: MatSeqAIJSetPreallocation(user->Av,2,NULL);
888: MatGetOwnershipRange(user->Av,&istart,&iend);
890: for (i=istart; i<iend; i++){
891: if (i<m/3){
892: iblock = i / (user->mx-1);
893: j = iblock*user->mx + (i % (user->mx-1));
894: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
895: j = j+1;
896: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
897: }
898: if (i>=m/3 && i<2*m/3){
899: iblock = (i-m/3) / (user->mx*(user->mx-1));
900: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
901: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
902: j = j + user->mx;
903: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
904: }
905: if (i>=2*m/3){
906: j = i-2*m/3;
907: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
908: j = j + user->mx*user->mx;
909: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
910: }
911: }
913: MatAssemblyBegin(user->Av,MAT_FINAL_ASSEMBLY);
914: MatAssemblyEnd(user->Av,MAT_FINAL_ASSEMBLY);
916: /* Generate transpose of averaging matrix Av */
917: MatTranspose(user->Av,MAT_INITIAL_MATRIX,&user->AvT);
919: MatCreate(PETSC_COMM_WORLD,&user->L);
920: MatSetSizes(user->L,PETSC_DECIDE,PETSC_DECIDE,m+n,n);
921: MatSetFromOptions(user->L);
922: MatMPIAIJSetPreallocation(user->L,2,NULL,2,NULL);
923: MatSeqAIJSetPreallocation(user->L,2,NULL);
924: MatGetOwnershipRange(user->L,&istart,&iend);
926: for (i=istart; i<iend; i++){
927: if (i<m/3){
928: iblock = i / (user->mx-1);
929: j = iblock*user->mx + (i % (user->mx-1));
930: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
931: j = j+1;
932: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
933: }
934: if (i>=m/3 && i<2*m/3){
935: iblock = (i-m/3) / (user->mx*(user->mx-1));
936: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
937: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
938: j = j + user->mx;
939: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
940: }
941: if (i>=2*m/3 && i<m){
942: j = i-2*m/3;
943: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
944: j = j + user->mx*user->mx;
945: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
946: }
947: if (i>=m){
948: j = i - m;
949: MatSetValues(user->L,1,&i,1,&j,&sqrt_beta,INSERT_VALUES);
950: }
951: }
953: MatAssemblyBegin(user->L,MAT_FINAL_ASSEMBLY);
954: MatAssemblyEnd(user->L,MAT_FINAL_ASSEMBLY);
956: MatScale(user->L,PetscPowScalar(h,1.5));
958: /* Generate Div matrix */
959: MatTranspose(user->Grad,MAT_INITIAL_MATRIX,&user->Div);
961: /* Build work vectors and matrices */
962: VecCreate(PETSC_COMM_WORLD,&user->S);
963: VecSetSizes(user->S, PETSC_DECIDE, user->mx*user->mx*(user->mx-1)*3);
964: VecSetFromOptions(user->S);
966: VecCreate(PETSC_COMM_WORLD,&user->lwork);
967: VecSetSizes(user->lwork,PETSC_DECIDE,m+user->mx*user->mx*user->mx);
968: VecSetFromOptions(user->lwork);
970: MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);
971: MatDuplicate(user->Av,MAT_SHARE_NONZERO_PATTERN,&user->Avwork);
973: VecCreate(PETSC_COMM_WORLD,&user->d);
974: VecSetSizes(user->d,PETSC_DECIDE,user->ndata*user->nt);
975: VecSetFromOptions(user->d);
977: VecDuplicate(user->S,&user->Swork);
978: VecDuplicate(user->S,&user->Av_u);
979: VecDuplicate(user->S,&user->Twork);
980: VecDuplicate(user->S,&user->Rwork);
981: VecDuplicate(user->y,&user->ywork);
982: VecDuplicate(user->u,&user->uwork);
983: VecDuplicate(user->u,&user->js_diag);
984: VecDuplicate(user->c,&user->cwork);
985: VecDuplicate(user->d,&user->dwork);
987: /* Create matrix-free shell user->Js for computing A*x */
988: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m*user->nt,user,&user->Js);
989: MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
990: MatShellSetOperation(user->Js,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
991: MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
992: MatShellSetOperation(user->Js,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
994: /* Diagonal blocks of user->Js */
995: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsBlock);
996: MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateMatBlockMult);
997: /* Blocks are symmetric */
998: MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockMult);
1000: /* Create a matrix-free shell user->JsBlockPrec for computing (U+D)\D*(L+D)\x, where JsBlock = L+D+U,
1001: D is diagonal, L is strictly lower triangular, and U is strictly upper triangular.
1002: This is an SSOR preconditioner for user->JsBlock. */
1003: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsBlockPrec);
1004: MatShellSetOperation(user->JsBlockPrec,MATOP_MULT,(void(*)(void))StateMatBlockPrecMult);
1005: /* JsBlockPrec is symmetric */
1006: MatShellSetOperation(user->JsBlockPrec,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockPrecMult);
1007: MatSetOption(user->JsBlockPrec,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1009: /* Create a matrix-free shell user->Jd for computing B*x */
1010: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m,user,&user->Jd);
1011: MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1012: MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);
1014: /* User-defined routines for computing user->Js\x and user->Js^T\x*/
1015: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m*user->nt,user,&user->JsInv);
1016: MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateMatInvMult);
1017: MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatInvTransposeMult);
1019: /* Solver options and tolerances */
1020: KSPCreate(PETSC_COMM_WORLD,&user->solver);
1021: KSPSetType(user->solver,KSPCG);
1022: KSPSetOperators(user->solver,user->JsBlock,user->JsBlockPrec);
1023: KSPSetInitialGuessNonzero(user->solver,PETSC_FALSE);
1024: KSPSetTolerances(user->solver,1e-4,1e-20,1e3,500);
1025: KSPSetFromOptions(user->solver);
1026: KSPGetPC(user->solver,&user->prec);
1027: PCSetType(user->prec,PCSHELL);
1029: PCShellSetApply(user->prec,StateMatBlockPrecMult);
1030: PCShellSetApplyTranspose(user->prec,StateMatBlockPrecMult);
1031: PCShellSetContext(user->prec,user);
1033: /* Create scatter from y to y_1,y_2,...,y_nt */
1034: PetscMalloc1(user->nt*user->m,&user->yi_scatter);
1035: VecCreate(PETSC_COMM_WORLD,&yi);
1036: VecSetSizes(yi,PETSC_DECIDE,user->mx*user->mx*user->mx);
1037: VecSetFromOptions(yi);
1038: VecDuplicateVecs(yi,user->nt,&user->yi);
1039: VecDuplicateVecs(yi,user->nt,&user->yiwork);
1041: VecGetOwnershipRange(user->y,&lo2,&hi2);
1042: istart = 0;
1043: for (i=0; i<user->nt; i++){
1044: VecGetOwnershipRange(user->yi[i],&lo,&hi);
1045: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_yi);
1046: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_y);
1047: VecScatterCreate(user->y,is_from_y,user->yi[i],is_to_yi,&user->yi_scatter[i]);
1048: istart = istart + hi-lo;
1049: ISDestroy(&is_to_yi);
1050: ISDestroy(&is_from_y);
1051: }
1052: VecDestroy(&yi);
1054: /* Create scatter from d to d_1,d_2,...,d_ns */
1055: PetscMalloc1(user->ns*user->ndata,&user->di_scatter);
1056: VecCreate(PETSC_COMM_WORLD,&di);
1057: VecSetSizes(di,PETSC_DECIDE,user->ndata);
1058: VecSetFromOptions(di);
1059: VecDuplicateVecs(di,user->ns,&user->di);
1060: VecGetOwnershipRange(user->d,&lo2,&hi2);
1061: istart = 0;
1062: for (i=0; i<user->ns; i++){
1063: VecGetOwnershipRange(user->di[i],&lo,&hi);
1064: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_di);
1065: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_d);
1066: VecScatterCreate(user->d,is_from_d,user->di[i],is_to_di,&user->di_scatter[i]);
1067: istart = istart + hi-lo;
1068: ISDestroy(&is_to_di);
1069: ISDestroy(&is_from_d);
1070: }
1071: VecDestroy(&di);
1073: /* Assemble RHS of forward problem */
1074: VecCopy(bc,user->yiwork[0]);
1075: for (i=1; i<user->nt; i++){
1076: VecSet(user->yiwork[i],0.0);
1077: }
1078: Gather_i(user->q,user->yiwork,user->yi_scatter,user->nt);
1079: VecDestroy(&bc);
1081: /* Compute true state function yt given ut */
1082: VecCreate(PETSC_COMM_WORLD,&user->ytrue);
1083: VecSetSizes(user->ytrue,PETSC_DECIDE,n*user->nt);
1084: VecSetFromOptions(user->ytrue);
1086: /* First compute Av_u = Av*exp(-u) */
1087: VecSet(user->uwork,0);
1088: VecAXPY(user->uwork,-1.0,user->utrue); /* Note: user->utrue */
1089: VecExp(user->uwork);
1090: MatMult(user->Av,user->uwork,user->Av_u);
1092: MatMatMultSymbolic(user->Div,user->Grad,PETSC_DEFAULT,&user->DSG);
1093: user->dsg_formed = PETSC_TRUE;
1095: /* Next form DSG = Div*S*Grad */
1096: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1097: MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1098: if (user->dsg_formed) {
1099: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1100: } else {
1101: MatMatMultSymbolic(user->Div,user->Grad,PETSC_DEFAULT,&user->DSG);
1102: MatMatMultNumeric(user->Div,user->Grad,user->DSG);
1103: user->dsg_formed = PETSC_TRUE;
1104: }
1105: /* B = speye(nx^3) + ht*DSG; */
1106: MatScale(user->DSG,user->ht);
1107: MatShift(user->DSG,1.0);
1109: /* Now solve for ytrue */
1110: StateMatInvMult(user->Js,user->q,user->ytrue);
1112: /* Initial guess y0 for state given u0 */
1114: /* First compute Av_u = Av*exp(-u) */
1115: VecSet(user->uwork,0);
1116: VecAXPY(user->uwork,-1.0,user->u); /* Note: user->u */
1117: VecExp(user->uwork);
1118: MatMult(user->Av,user->uwork,user->Av_u);
1120: /* Next form DSG = Div*S*Grad */
1121: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1122: MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1123: if (user->dsg_formed) {
1124: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1125: } else {
1126: MatMatMultSymbolic(user->Div,user->Grad,PETSC_DEFAULT,&user->DSG);
1127: MatMatMultNumeric(user->Div,user->Grad,user->DSG);
1128: user->dsg_formed = PETSC_TRUE;
1129: }
1130: /* B = speye(nx^3) + ht*DSG; */
1131: MatScale(user->DSG,user->ht);
1132: MatShift(user->DSG,1.0);
1134: /* Now solve for y */
1135: StateMatInvMult(user->Js,user->q,user->y);
1137: /* Construct projection matrix Q, a block diagonal matrix consisting of nt copies of Qblock along the diagonal */
1138: MatCreate(PETSC_COMM_WORLD,&user->Qblock);
1139: MatSetSizes(user->Qblock,PETSC_DECIDE,PETSC_DECIDE,user->ndata,n);
1140: MatSetFromOptions(user->Qblock);
1141: MatMPIAIJSetPreallocation(user->Qblock,8,NULL,8,NULL);
1142: MatSeqAIJSetPreallocation(user->Qblock,8,NULL);
1144: for (i=0; i<user->mx; i++){
1145: x[i] = h*(i+0.5);
1146: y[i] = h*(i+0.5);
1147: z[i] = h*(i+0.5);
1148: }
1150: MatGetOwnershipRange(user->Qblock,&istart,&iend);
1151: nx = user->mx; ny = user->mx; nz = user->mx;
1152: for (i=istart; i<iend; i++){
1153: xri = xr[i];
1154: im = 0;
1155: xim = x[im];
1156: while (xri>xim && im<nx){
1157: im = im+1;
1158: xim = x[im];
1159: }
1160: indx1 = im-1;
1161: indx2 = im;
1162: dx1 = xri - x[indx1];
1163: dx2 = x[indx2] - xri;
1165: yri = yr[i];
1166: im = 0;
1167: yim = y[im];
1168: while (yri>yim && im<ny){
1169: im = im+1;
1170: yim = y[im];
1171: }
1172: indy1 = im-1;
1173: indy2 = im;
1174: dy1 = yri - y[indy1];
1175: dy2 = y[indy2] - yri;
1177: zri = zr[i];
1178: im = 0;
1179: zim = z[im];
1180: while (zri>zim && im<nz){
1181: im = im+1;
1182: zim = z[im];
1183: }
1184: indz1 = im-1;
1185: indz2 = im;
1186: dz1 = zri - z[indz1];
1187: dz2 = z[indz2] - zri;
1189: Dx = x[indx2] - x[indx1];
1190: Dy = y[indy2] - y[indy1];
1191: Dz = z[indz2] - z[indz1];
1193: j = indx1 + indy1*nx + indz1*nx*ny;
1194: v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1195: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1197: j = indx1 + indy1*nx + indz2*nx*ny;
1198: v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1199: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1201: j = indx1 + indy2*nx + indz1*nx*ny;
1202: v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1203: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1205: j = indx1 + indy2*nx + indz2*nx*ny;
1206: v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1207: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1209: j = indx2 + indy1*nx + indz1*nx*ny;
1210: v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1211: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1213: j = indx2 + indy1*nx + indz2*nx*ny;
1214: v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1215: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1217: j = indx2 + indy2*nx + indz1*nx*ny;
1218: v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1219: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1221: j = indx2 + indy2*nx + indz2*nx*ny;
1222: v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1223: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1224: }
1225: MatAssemblyBegin(user->Qblock,MAT_FINAL_ASSEMBLY);
1226: MatAssemblyEnd(user->Qblock,MAT_FINAL_ASSEMBLY);
1228: MatTranspose(user->Qblock,MAT_INITIAL_MATRIX,&user->QblockT);
1229: MatTranspose(user->L,MAT_INITIAL_MATRIX,&user->LT);
1231: /* Add noise to the measurement data */
1232: VecSet(user->ywork,1.0);
1233: VecAYPX(user->ywork,user->noise,user->ytrue);
1234: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
1235: for (j=0; j<user->ns; j++){
1236: i = user->sample_times[j];
1237: MatMult(user->Qblock,user->yiwork[i],user->di[j]);
1238: }
1239: Gather_i(user->d,user->di,user->di_scatter,user->ns);
1241: /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1242: KSPSetFromOptions(user->solver);
1243: PetscFree(x);
1244: PetscFree(y);
1245: PetscFree(z);
1246: return(0);
1247: }
1249: PetscErrorCode ParabolicDestroy(AppCtx *user)
1250: {
1252: PetscInt i;
1255: MatDestroy(&user->Qblock);
1256: MatDestroy(&user->QblockT);
1257: MatDestroy(&user->Div);
1258: MatDestroy(&user->Divwork);
1259: MatDestroy(&user->Grad);
1260: MatDestroy(&user->Av);
1261: MatDestroy(&user->Avwork);
1262: MatDestroy(&user->AvT);
1263: MatDestroy(&user->DSG);
1264: MatDestroy(&user->L);
1265: MatDestroy(&user->LT);
1266: KSPDestroy(&user->solver);
1267: MatDestroy(&user->Js);
1268: MatDestroy(&user->Jd);
1269: MatDestroy(&user->JsInv);
1270: MatDestroy(&user->JsBlock);
1271: MatDestroy(&user->JsBlockPrec);
1272: VecDestroy(&user->u);
1273: VecDestroy(&user->uwork);
1274: VecDestroy(&user->utrue);
1275: VecDestroy(&user->y);
1276: VecDestroy(&user->ywork);
1277: VecDestroy(&user->ytrue);
1278: VecDestroyVecs(user->nt,&user->yi);
1279: VecDestroyVecs(user->nt,&user->yiwork);
1280: VecDestroyVecs(user->ns,&user->di);
1281: PetscFree(user->yi);
1282: PetscFree(user->yiwork);
1283: PetscFree(user->di);
1284: VecDestroy(&user->c);
1285: VecDestroy(&user->cwork);
1286: VecDestroy(&user->ur);
1287: VecDestroy(&user->q);
1288: VecDestroy(&user->d);
1289: VecDestroy(&user->dwork);
1290: VecDestroy(&user->lwork);
1291: VecDestroy(&user->S);
1292: VecDestroy(&user->Swork);
1293: VecDestroy(&user->Av_u);
1294: VecDestroy(&user->Twork);
1295: VecDestroy(&user->Rwork);
1296: VecDestroy(&user->js_diag);
1297: ISDestroy(&user->s_is);
1298: ISDestroy(&user->d_is);
1299: VecScatterDestroy(&user->state_scatter);
1300: VecScatterDestroy(&user->design_scatter);
1301: for (i=0; i<user->nt; i++){
1302: VecScatterDestroy(&user->yi_scatter[i]);
1303: }
1304: for (i=0; i<user->ns; i++){
1305: VecScatterDestroy(&user->di_scatter[i]);
1306: }
1307: PetscFree(user->yi_scatter);
1308: PetscFree(user->di_scatter);
1309: PetscFree(user->sample_times);
1310: return(0);
1311: }
1313: PetscErrorCode ParabolicMonitor(Tao tao, void *ptr)
1314: {
1316: Vec X;
1317: PetscReal unorm,ynorm;
1318: AppCtx *user = (AppCtx*)ptr;
1321: TaoGetSolutionVector(tao,&X);
1322: Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1323: VecAXPY(user->ywork,-1.0,user->ytrue);
1324: VecAXPY(user->uwork,-1.0,user->utrue);
1325: VecNorm(user->uwork,NORM_2,&unorm);
1326: VecNorm(user->ywork,NORM_2,&ynorm);
1327: PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
1328: return(0);
1329: }
1332: /*TEST
1334: build:
1335: requires: !complex
1337: test:
1338: args: -tao_cmonitor -tao_type lcl -ns 1 -tao_gatol 1.e-4 -ksp_max_it 30
1339: requires: !single
1341: TEST*/